Esercizio
$\frac{x^4-6x^3+7x^2+22x-22}{x-4}\:$
Soluzione passo-passo
1
Dividere $x^4-6x^3+7x^2+22x-22$ per $x-4$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-4;}{\phantom{;}x^{3}-2x^{2}-x\phantom{;}+18\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-4\overline{\smash{)}\phantom{;}x^{4}-6x^{3}+7x^{2}+22x\phantom{;}-22\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-4;}\underline{-x^{4}+4x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+4x^{3};}-2x^{3}+7x^{2}+22x\phantom{;}-22\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n;}\underline{\phantom{;}2x^{3}-8x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{3}-8x^{2}-;x^n;}-x^{2}+22x\phantom{;}-22\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n;}\underline{\phantom{;}x^{2}-4x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}x^{2}-4x\phantom{;}-;x^n-;x^n;}\phantom{;}18x\phantom{;}-22\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n-;x^n;}\underline{-18x\phantom{;}+72\phantom{;}\phantom{;}}\\\phantom{;;;-18x\phantom{;}+72\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}50\phantom{;}\phantom{;}\\\end{array}$
$x^{3}-2x^{2}-x+18+\frac{50}{x-4}$
Risposta finale al problema
$x^{3}-2x^{2}-x+18+\frac{50}{x-4}$